Light Focusing through Dynamic Media via Real-Valued Intensity Transmission Matrix

TL;DR

The paper tackles the problem of focusing light through dynamic, scattering tissue by introducing a real-valued intensity transmission matrix (RVITM) that enables high-speed wavefront shaping. By encoding amplitude and phase into a real-valued matrix, RVITM reduces the measurement burden to $2N$, and can be further shortened to $N$ or $N/2$ patterns, trading static focus enhancement for speed. Systematic experiments across static diffusers, moving diffusers, and ex vivo tissues reveal a clear speed–enhancement trade-off governed by the decorrelation time $\tau_c$, with guidance on configuring RVITM for varying dynamics. The results demonstrate practical focusing at decorrelation times as short as $\tau_c\approx10-13$ ms and runtime as low as $\approx31$ ms, supporting adaptive, non-invasive optical control in biomedical contexts and guiding future integration with faster modulators and non-invasive guidestars like photoacoustics.

Abstract

Precise light delivery through biological tissue is essential for deep-tissue imaging and phototherapeutic applications. Wavefront shaping enables control over scattered light by modulating the incident wavefront, but its application in living tissue is hindered by tissue-induced temporal decorrelation. This study systematically investigated the real-valued intensity transmission matrix (RVITM), a high-speed wavefront shaping method, for light focusing across a broad range of speckle decorrelation times. The inherent trade-off between static light focusing enhancement and implementation speed is characterized, which provided practical guidelines for implementing RVITM in real-time wavefront shaping under varying dynamic conditions. Effective optical focusing using a RVITM with 33 ms runtime was achieved through porcine liver with decorrelation times as short as 13 ms, demonstrating feasibility for biologically relevant dynamics and supporting the development of adaptive, non-invasive optical control for biomedical applications.

Figures (6)

• Figure 1: Illustrative diagram of RVITM-based wavefront shaping for light focusing through disordered media. A series of binary Hadamard patterns is used to characterize the scattering medium. After capturing a set of input (DMD patterns) and output (light intensities) pairs, RVITM connected the input light intensities to the output light intensities at the target position (focus). In the focusing step, the optimal DMD pattern was determined by turning 'ON' all the DMD micromirrors that cause constructive interference at the target position, thus focusing the light. DAQ: data acquisition card.
• Figure 2: Measurement of speckle decorrelation time in dynamic media. (a) Moving diffuser setup. (b) Correlation coefficient between the speckle patterns over time, when a 2 mm thick diffuser was moved at 0.40 mm/s. Speckle decorrelation time $\tau_{c}$ = 13 ms was determined for this speed.
• Figure 3: Experimental setup and workflow of RVITM-based wavefront shaping system. (a) Schematic of the experimental setup. L$_{1-3}$, convex lenses; DMD, digital micromirror device; PH, pinhole. (b) Workflow of the high-speed wavefront shaping system using full 2N scheme, reduced N and N/2 scheme for focusing light through scattering medium, N = 1024.
• Figure 4: Focusing performance of RVITM through static media. (a) - (c) The focus in the image plane after (a) RVITM modulation (2N measurements), (b) RVITM modulation (N measurements), (c) RVITM modulation (N/2 measurements). (d) - (f) Cross section profile at the largest pixel value of the focus image in (a) - (c). (g) System runtime for different mode and number of measurements settings. (h) Focus enhancement for different mode and number of measurements settings. Scale bar is 50 µm.
• Figure 5: Light focusing performance through dynamic diffusers. (a) The static focus image taken by the CCD camera and the black dash-line shows the region along which 1D profiles are obtained by scanning. Scale bar: 50µm. (b) - (d) The 1D profile across the line from P1 to P2, as shown in panel (a), after continuous RVITM optimization with 2N, N, N/2 measurements when the diffuser is moved on a translational stage to create a series of different correlation times. (e) - (g) Curves of focus enhancement with speckle decorrelation time for different number of measurements with e) 4096 input modes, (f) 1024 input modes and g) 256 input modes. (h) - (i) Curves of focus enhancement with speckle decorrelation time for different number of input modes with same number of measurements: (h) 2048 measurements and (i) 512 measurements.